1. Field of the Invention
This invention relates to the field of seismology and in particular to the processing of seismic reflection data to render them more useful in interpreting the geophysical characteristics of the earth. Specifically, this disclosure involves a new method and apparatus for multidimensional amplitude scaling of seismic traces such that further processing and/or displaying of the traces will result in a seismic section of improved resolution.
2. Description of the Prior Art
It is well known and documented that during the course of a seismic survey, such as the mapping of geological structures by creating seismic waves and observing the arrival times of the waves reflected from acoustic-impedance contrasts or refracted through high-velocity members, the amplitude of a seismic signal decays as it propagates through the earth. Further, this amplitude decay will be frequency dependent in that the higher frequency components tend to suffer greater amplitude attenuation particularly at later arrival times. Generally several factors are viewed as contributing to the amplitude attenuation such as geometrical spreading, reflection absorption, scattering and various other transmission loss mechanisms.
This amplitude decay typically has been compensated for by application of an inverse gain correction in the form of a programmed gain curve, automatic gain control circuit, or other similar method. Such methods correct for amplitude decay as a function of time over the time span of the seismic trace by systematically amplifying the later arriving signals. Additionally, a family of gain corrections keyed to the source-to-receiver distance are sometimes applied, resulting in a scaling as a function of time and position. However, this amplitude scaling, intended to compensate for signal attenuation, historically has been performed independent of frequency; the seismic trace is not resolved into frequency components but scaled as a whole by a single inverse gain curve.
Although it is recognized that amplitude attenuation occurs as a function of frequency as well as other variables, very little has been published as to various possible methods and criteria of accounting for and correcting for the signal decay as a function of frequency. One exception to this is found in U.S. Pat. No. 3,327,805 Glazier et al. A system for processing seismic signals is described and claimed involving separation of a seismic reflection signal created by a seismic disturbance of known amplitude vs. frequency spectrum into a series of one cycle per second wide frequency bands. In the process of separating into narrow frequency bands the amplitudes are adjusted to a constant value. These components are then weighted and recombined such that the recombination has the same frequency force spectrum as did the known seismic disturbance. Thus, the frequency spectrum is normalized in the sense that the amplitude as a function of frequency is restored to the same relative value as that of the original seismic disturbance. The advantage of this process lies in the selective removal of the unwanted lower frequencies containing surface noise and ground roll. One of the disadvantages of this process is that the high frequency components which are to be amplified have relatively unfavorable signal-to-noise ratios, thus selective amplification actually introduces background noise at the high frequencies. Hence, the process is useful only over a rather narrow frequency range.
In U.S. Pat. No. 3,454,924 by Sherwood et al the problem of introducing high frequency noise was explicitly recognized. The upper frequency limits for their adaptive gain control process were identified as 50 cycles per second for the early part of the seismic trace and about 35 cycles per second for later times. Sherwood et al proposed that beyond these limits the high frequency content should be made to decline. In contrast, the present invention explicitly involves the amplification of the high frequency components over a frequency range well in excess of the upper limits suggested by Sherwood et al. This is a direct contradiction of what the cited art is suggesting with respect to the presence of high frequency noise.
Additionally, Sherwood et al essentially ignores the significance of zero-phase filtering while Glazier et al recognizes the desirability of no phase distortion, but bypasses the problem in a manner which is inconsistent with the multidimensional amplitude scaling of the present invention. Specifically, Glazier et al simulates zero-phase filtering by separating the seismic signal into very narrow frequency bandpasses. By using essentially 1 Hz bandwidths the filter will appear to be approximately linear across this frequency range independent of which frequency is to be passed. Thus, by making independent static time corrections on each of these bandpasses, the overall zero-phase filtering is simulated. However, approximating zero-phase filtering by separating the seismic trace into frequency bandwidths of 5 Hz or less is deleterious to the desired improved resolution of present invention even if this filter in fact is zero-phase-shift.
Such processes as described by Glazier et al and Sherwood et al have historically been viewed as methods of selectively biasing certain undesirable low frequency noises, particularly ground roll. Hence the term "automatic spectrum whitening" has been used to describe these processes as witnessed in U.S. Pat. No. 3,812,457 by Weller. However, the spectrum whitening of the present invention is a far more sophisticated concept than that of this prior art. The spectral amplitude flattening by selective removal of undesired frequency components within the classical seismic frequency range is not the same as the multidimensional amplitude scaling of the present disclosure. It is the contention of present application that the combination of spectral amplitude flattening and broadening to high frequencies both being performed under a zero-phase-shift constraint results in a type of whitening that has inherent wave compression and deconvolution aspects. Consequently, this leads to improved resolution without destroying coherency between events on adjacent seismic traces. It is interesting to note that in Weller's patent the time dependency of amplitude attenuation has to be completely ignored and the cited art should be viewed as teaching amplitude-frequency scaling independent of time because Weller does not use a seismic source signal but rather makes a purely random noise observation, further indicating that the art does not fully recognize how significant a tool proper multidimensional amplitude scaling can be.
Another method of recognizing amplitude decay as a function of time and frequency which leads to an alternate basis for correcting for attenuation is to perform a Fourier analysis of the seismic data and view the phenomenon in a frequency domain. In particular it is observed that the frequency content along the length of the record will shift to lower frequencies as the time increases. This corresponds to the previous interpretation that higher frequency seismic signals are attenuated at a faster rate than lower frequency seismic signals. Thus, the earlier recorded seismic reflections, which represent the shallow subsurface formations, have a higher mean frequency than the later recorded seismic reflections which represent the deep surface formations.
The recognition of this shift in the center frequency as a function of time led to the proposal in U.S. Pat. No. 3,281,776 by Ruehle that in processing seismic data one should employ a time-domain filter comprising a plurality of heads spaced one from the other with means to cause the heads to move continuously to effect filters of different bandpass. Later, in U.S. Pat. No. 3,716,829 again by Ruehle a computer performed method is disclosed which quantitatively uses the center frequencies along a seismic trace to create a frequency shift which supposedly accounts for attenuation of high frequency reflections. In both of these methods the information or knowledge which is introduced at the high frequencies to compensate for the attenuation does not correspond to the information which was originally characteristic of that frequency. In contrast, direct multidimensional amplitude scaling in the time domain preserves the integrity of the information as a function of frequency.
Still other methods have been proposed for compensating for distortion and thus creating wide band representation involving processes that are less than multidimensional scaling. For example in U.S. Pat. No. 3,715,715 by Ruehle a computer performed method for obtaining a wide band representation is claimed. This method involves calculating a mean spectral amplitude for successive Fourier analyses of successive truncations of the seismic trace to obtain an average amplitude as a function of time. This average amplitude function is then used in an inverse filtering process as described in U.S. Pat. No. 3,275,980 by Foster. Again, the correction is made essentially independent of frequency and amounts to a computerized version of the gain curve techniques known in the art.
Additionally, other techniques are known involving narrow frequency bands but for purposes other than correcting for amplitude attenuation. See for example U.S. Pat. Nos. 3,259,878 and 3,349,860 by Mifsud. In U.S. Pat. No. 3,259,878 a set of elemental signals each having narrow frequency bands is used individually as a seismic source creating a set of received signals characteristic of the respective frequencies. A total source signal having the desired frequency spectrum is then synthesized by first adjusting the element source signals in terms of both relative phase and amplitude and then summing them together. Having thus determined the adjustments required to create the desired total source signal these same adjustments are then applied to the respective received signals and summed together to yield a total received signal. This total signal can then be processed as a seismic trace in manners known to the art. However, there is no suggestion or criterion set forth that would account for amplitude attenuation during the adjusting procedure. In U.S. Pat. No. 3,349,860 a process is described wherein subsets of individual detectors within a group are assigned narrow frequency ranges and specific geometrical locations for the purpose of achieving the same directivity pattern for all frequencies. Again no attempt is made to correct for amplitude attenuation. In fact in U.S. Pat. No. 3,292,143 by Russell amplitude decay as a function of frequency and time is recognized without attempting to make any scaling of the trace. Instead the change in relative frequency content during seismic exploration is utilized to identify the rock formation.
Frequency dependent absorption with depth (i.e., time of arrival) not ony creates problems in interpreting observed seismic reflections but also has an analogous influence when one attempts to construct "a priori" a synthetic seismogram. For a theoretical discussion of the effect of frequency and depth dependent absorption when building a theoretical seismogram see "Theoretical Seismograms with Frequency and Depth Dependent Absorption" by A. W. Trovey in Geophysics, Vol. 27, p. 766-785 (1962). In this article it is concluded that a time-domain calculation is preferred in that a solution by Fourier Transform in the frequency domain would lead to the introduction of significant error.